Seems I'm late to the party. OK, first of all, there's this (bold emphasis mine):

Compare different sensor generations and everything [noise equivalence] breaks down, though advocates of this equivalence never use the equivalence when comparing full frame sensors of different generations.

Well, duh. Does anyone object to saying that 50mm f/2 on an EM5 is equivalent to 50mm f/2 on an EP-1, even though the EM5 will capture a photo with more detail and have less noise due to a more efficient sensor with more pixels?

No, of course not.

Thus, the fact that 50mm f/2 on mFT does not necessarily have the exact same noise as 100mm f/4 on FF for the same shutter speed, due to differences in sensor efficiency, has no bearing on the statement that 50mm f/2 on mFT is equivalent to 100mm f/4 on FF.

A 50mm f/2 lens is a 50mm f/2 lens regardless of the sensor that sits behind it. However, the effect of 50mm f/2, in terms of the visual properties of the recorded photo, depend very much on the sensor that sits behind the lens:

The photos all have the same motion blur and the same total amount of light falls on the sensor when the aperture diameter and shutter speed are the same (e.g. ISO 100 on mFT, ISO 160 on APS-C, and ISO 400 on FF).

The photos all have the same same noise when the same total amount of light falls on the sensor if the sensors are equally efficient (less noise if the sensor is more efficient, more noise if the sensor is less efficient).

Other elements of IQ, such as resolution, bokeh, flare resistance, etc., as well as elements of operation, such as AF speed/accuracy, size, weight, etc., are not covered in this use of the term "equivalent".

The biggest issue I have with all the equivalency talk is that it treats the 35mm size as some sort of magical reference format where lenses act their ‘true’ self.

Absolutely untrue. There is nothing special about 35mm in terms of Equivalence. It is a format, like any other, and due to its popularity with film, it is used today as the reference format, but we don't need a reference format at all. We could make mFT the reference format, and then the crop factor between mFT and FF would be 0.5x instead of 2x. Same difference.

Next up:

I’ve heard many times “Yeah, your 75mm f/1.8 is crap – it’s like a 150mm f/3.6.” No, it’s not, it’s a 75mm lens with an f/1.8 aperture and a field of view that is the same as a 150mm lens on full frame.

What IS true is that the 75mm f/1.8 is not capable of the same ultra shallow depth of field as, say, something like the Canon 135mm f/2L on full frame. However, this is essentially the ONLY way that it is inferior. It passes the same amount of light, and it exposes as an f/1.8 lens because it IS an f/1.8 lens.

Well, no, the 75 / 1.8 is not "crap", but it is equivalent to a 150 / 3.6 on FF. And, yes, that's not merely in terms of AOV and DOF, but also in terms of how much light falls on the sensor for a given shutter speed -- something the author has apparently forgotten that he acknowledged on the previous page.

Next up:

Those who harp on aperture equivalence as it relates to shallow depth of field also IGNORE all the BENEFITS to having more depth of field for the same aperture.

The only benefit to "having more depth of field for the same aperture" is if you want more DOF, and typically shoot in an AE (auto exposure) mode where you let the camera choose the f-ratio for you -- the smaller format camera will typically choose a deeper DOF. However, this is simply a matter of firmware, and has nothing to do with any actual differences between the formats.

Next we have:

Given that my lenses give me shallow enough depth of field for most anything I could ever want, and image quality is absolutely good enough for most any size print I make, I simply get to save 12 lbs of gear in my bag for the same apertures and field of view.

Well, as we all know, the same apertures (f-ratios) on different systems have very different results, just as the same focal length on different systems have very different results, so...

Indeed, the author might want to save a few more pounds (and a lot of money) by getting an XZ-2 with its f/1.8-2.5 lens if shooting "the same apertures and field of view" is such a bonus.

As for "saving 12 lbs of gear", well, I'd be curious what he was packing:

Maybe he shot long telephoto? Well, the Panasonic FZ200 is worth a look, especially if you want "f/2.8" out to "600mm". Equivalence doesn't apply just between mFT and FF, don't you know.

Lastly, we have:

So, those of you who keep hammering on this ‘equivalence talk’, please stop. We’ve already made the decision to forgo extremely shallow depth of field by our choice of cameras. Since that is the ONLY situation where aperture equivalence has any relevence whatsoever, it’s pretty much a moot point.

No, shallow DOF is not the only difference between FF and mFT. That said:

Equivalence says nothing about shallow DOF being superior to deep DOF, as this is entirely subjective.

Equivalence makes no claims whatsoever about which system is superior to another system, especially given that there are so many aspects about systems that Equivalence does not address. For example, in terms of IQ, Equivalence says nothing about bokeh, moiré, distortion, color, etc., and in terms of operation, Equivalence says nothing about AF, build, features, etc. In fact, Equivalence can even work against larger sensor systems by denying them their "noise advantage" when they need to match both the DOF and shutter speed of smaller sensor systems.

So, those of you who keep hammering on about Equivalence might want to get a bit more familiar about what Equivalence says, and what it doesn't.